Satellite positioning has been widely used in various applications. In satellite communication systems such as Global Navigation Satellite System (GNSS), a cold start state means that no information such as the receiver position, observation time, satellite orbit information (e.g. almanac or ephemeris) are available. Accordingly, the identification (ID) of a visible satellite is of course unknown. In addition to the satellite ID, the Doppler frequency due to the satellite motion with respect to the user is unknown. If a Code Division Multiple Access (CDMA) signaling is used in the system, Global Positioning System (GPS) for example, the code phase of the Pseudo Random Noise (PRN) code used by a satellite is also required to track that satellite. As mentioned, the characteristic of a satellite signal can be determined by the following variables: satellite ID, Doppler frequency and PRN code phase.
At least four satellites are required to fix a three dimensional position. The required time-to-first-fix (TTFF) depends on how fast the four visible satellites can be found. For example, there may be as many as twelve GPS satellites that are visibly observed from the surface of the earth. Conventionally, all of the possible satellites are searched sequentially in order to find the visible satellites. Moreover, the Doppler frequency and PRN code phase of each satellite are also unknown. Therefore, it takes a lot of time to try all the possible values to determine a satellite's existence.
In general, a receiver searches for a visible satellite by using correlation analysis which considers satellite ID (e.g. satellites of the system GPS, Galileo, WAAS, EGNOS, MSAS etc.), code phase, and Doppler frequency. In addition, serial and parallel searches might be used. For example, four different satellites can be searched at the same time if there are four available channels. To search a satellite, all the possible code phases and Doppler frequencies thereof should be scanned.
A numerical example will be described hereinafter. Assuming that a visible GPS satellite list is {5, 9, 14, 15, 18, 21, 22, 26, 29, 30} for a receiver, which can use one physical channel and ten channels to search and track satellites, respectively. Scanning time, Ts, is defined as the time required to scan the whole range of possible Doppler frequencies and code phases. If a candidate satellite is not visible, a correlator misses it after searching time Ts. On the other hand, the correlator hits a visible satellite after searching time ½ Ts on average. Further, it is assumed that the data demodulation bit error rate is zero. Therefore, it takes 750 sec to receive almanac after the hit of the first satellite. After the hit of one satellite, it takes 27.6 sec on average to receive its ephemeris. The scanning time, Ts, can be computed for a receiver that tracks GPS L1 C/A code signal, which has 1023 chips per code period. If the code resolution of code correlation in acquisition process is ½ chip, the code phase uncertainty range size is 2046. In general, a combination of coherent and incoherent integration is used in the receiver to increase the acquisition sensitivity. Therefore, the correlation period (denoted by ΔT) for one particular pair of Doppler frequency and code phase candidates is the coherent time (denoted by Tc) multiplied by the incoherent count (denoted by Ti). Moreover, the Doppler frequency resolution, dF, is set to be 1/Tc in general. Finally, the whole Doppler range is denoted by ΔF. Based on the above assumptions, the scanning time Ts can be computed as follows.
                                                                        T                s                            =                              2046                ×                                                      Δ                    ⁢                                                                                  ⁢                    F                                    dF                                ×                Δ                ⁢                                                                  ⁢                T                                                                                        =                              2046                ×                                                      Δ                    ⁢                                                                                  ⁢                    F                                                        1                                          T                      C                                                                      ×                                  (                                                            T                      i                                        ×                                          T                      C                                                        )                                                                                                        =                              2046                ×                Δ                ⁢                                                                  ⁢                F                ×                                  T                  i                                ×                                  T                  C                  2                                                                                        (        1        )            If the receiver uses Tc of 1 ms to perform coherent integration and no incoherent integration is used, i.e., Ti equals one, then the required scanning time Ts is 20.46 seconds to scan the Doppler range size equal to 10 kHz. Four satellites must be found to make the first position fix. Assuming that the satellite search order is 1, 2, . . . , 32 for a sequential search of GPS satellites, then satellites 5, 9, 14 and 15 in the visible satellite list should be hit in order. Table 1 shows the results of sequential search.
TABLE 1Hit results of sequential searchSV ID12345678910111213141516Epoch (Ts)12344.55.56.57.58910111212.51314Hit0000100020000340SV ID1718192021222324252627282930Epoch (Ts)1515.516.517.51818.519.520.521.522232424.525Hit050067000800910
The visibilities of + the respective satellites can be obtained from observation statistics results at various time sampling points for a fixed position. FIG. 3 shows an example of observation time sampling points at a certain position. For instances, at observation time sampling point “8” of the diagram, the visible satellites are SV5, 9, 14, 15, 18, 21, 22, 26, 29 and 30.
As can be seen from Table 1, the sequential searching scheme takes 4.5 Ts (=110.07 sec) to achieve the first hit (Satellite 5 is hit), and about 13Ts+27.6=345.58 sec to achieve the first fix (Satellites 5, 9, 14 and 15 are hit and 27.6 sec are required to collect the ephemeris of satellite 15.) To find all satellites on the visible satellite list, 25 Ts (611.5 sec) is required. These periods of hit time are undesirably long. Accordingly, there is a need for a solution to reduce the time required to find the visible satellites.